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# M23-10

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Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128915 [0], given: 12183

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16 Sep 2014, 01:18
Expert's post
2
This post was
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Difficulty:

25% (medium)

Question Stats:

83% (00:52) correct 17% (00:42) wrong based on 29 sessions

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There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128915 [0], given: 12183

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128915 [0], given: 12183

### Show Tags

16 Sep 2014, 01:18
Expert's post
1
This post was
BOOKMARKED
Official Solution:

There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

The number of red roses must be a multiple of 21. It cannot be 42 or larger because this would mean that the number of white roses is 8 or larger and the total number of roses is 50 or larger. Because there are only 48 roses in the garden, the number of red roses is 21 and the number of white roses is 4. The number of black roses $$= 48 - 21 - 4 = 23$$.

_________________

Kudos [?]: 128915 [0], given: 12183

Intern
Joined: 24 Oct 2016
Posts: 29

Kudos [?]: 5 [0], given: 23

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30 Sep 2017, 23:42
This is a high quality question.

Kudos [?]: 5 [0], given: 23

Senior Manager
Joined: 25 Feb 2013
Posts: 407

Kudos [?]: 174 [0], given: 31

Location: India
GPA: 3.82

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01 Oct 2017, 00:42
Bunuel wrote:
There are 48 roses in a garden. Each of them is either black, red, or white. If the ratio of the number of red roses to the number of white roses is 21:4, how many black roses are there in the garden?

A. 4
B. 6
C. 21
D. 23
E. the data is not sufficient to answer the question

let the red and white roses be $$21x$$ & $$4x$$

Hence Black rose $$= 48-(21x+4x) = 48-25x$$

Now $$x=1$$, because at $$x=2$$, no of black roses will be negative which is not possible

Hence no of black rose $$= 48-25=23$$

Option $$D$$

Kudos [?]: 174 [0], given: 31

M23-10   [#permalink] 01 Oct 2017, 00:42
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# M23-10

Moderators: Bunuel, Vyshak

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